A special gas mixture is used in bacterial growth chambers which contains 5.00% by mass of CO2 and 95.0% O2. If the mole fraction of CO2 and O2 in the mixture is 0.0998 and 0.2340, respectively. What is the partial pressure in atmospheres of O2 and CO2 gases at a total pressure of 0.6880 atm?
CO2 = 0.0687 atm and O2 = 0.161 atm
CO2 = 0.000494 atm and O2 = 0.2223 atm
CO2 = 0.6536 atm and O2 = 0.0344 atm
CO2 = 0.0998 atm and O2 = 0.2340 atm
The correct answer is: CO2 = 0.0687 atm and O2 = 0.161 atm.
To solve this problem, we first need to find the partial pressure of each gas in the mixture. We can use the mole fraction and total pressure to do this.
Partial pressure of CO2 = 0.0998 x 0.6880 atm = 0.0687 atm
Partial pressure of O2 = 0.2340 x 0.6880 atm = 0.161 atm
Therefore, the correct answer is option A: CO2 = 0.0687 atm and O2 = 0.161 atm.
To solve this problem, we can use the concept of mole fraction and partial pressure.
First, let's convert the mole fractions to mass fractions using the given information about the gas mixture composition.
The mole fraction of CO2 is 0.0998, which means that it consists of 9.98% of the total moles in the mixture.
Similarly, the mole fraction of O2 is 0.2340, which means that it consists of 23.4% of the total moles in the mixture.
Next, let's calculate the mass fraction of CO2 and O2 using the given percentages.
The gas mixture contains 5.00% by mass of CO2, so the mass fraction of CO2 is 0.05.
The gas mixture contains 95.0% by mass of O2, so the mass fraction of O2 is 0.95.
Now, we can find the mole fraction of CO2 and O2 based on their mass fractions using the molecular weight of each gas.
The molecular weight of CO2 is approximately 44.01 g/mol, and the molecular weight of O2 is approximately 32.00 g/mol.
The mass of CO2 in the mixture can be calculated by multiplying the mass fraction by the total mass of the mixture. Assuming we have 100 grams of the mixture, the mass of CO2 is 0.05 * 100 grams = 5 grams.
The number of moles of CO2 can be calculated by dividing the mass of CO2 by its molecular weight: 5 grams / 44.01 g/mol = 0.1135 mol.
Similarly, the mass of O2 in the mixture is 0.95 * 100 grams = 95 grams.
The number of moles of O2 can be calculated by dividing the mass of O2 by its molecular weight: 95 grams / 32.00 g/mol = 2.9688 mol.
Now, we can calculate the partial pressure of CO2 and O2 using their mole fractions and the total pressure.
The partial pressure of CO2 is given by the mole fraction of CO2 multiplied by the total pressure: 0.0998 * 0.6880 atm = 0.0687 atm.
The partial pressure of O2 is given by the mole fraction of O2 multiplied by the total pressure: 0.2340 * 0.6880 atm = 0.161 atm.
Therefore, the partial pressure of CO2 is 0.0687 atm and the partial pressure of O2 is 0.161 atm.
So, the correct answer is CO2 = 0.0687 atm and O2 = 0.161 atm.